Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}2x-2y &= 5 \\ x+2y &= 6\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $x = {-2y+6}$ Substitute this expression for $x$ in the first equation. $2({-2y + 6}) - 2y = 5$ $-4y + 12 - 2y = 5$ Simplify by combining terms, then solve for $y$ $-6y + 12 = 5$ $-6y = -7$ $y = \dfrac{7}{6}$ Substitute $\dfrac{7}{6}$ for $y$ in the top equation. $2x-2( \dfrac{7}{6}) = 5$ $2x-\dfrac{7}{3} = 5$ $2x = \dfrac{22}{3}$ $x = \dfrac{11}{3}$ The solution is $\enspace x = \dfrac{11}{3}, \enspace y = \dfrac{7}{6}$.